Answers:
- What is that positive integer? 400
- What is the value of the positive root? 20
- What is the value of the negative root? -20
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Explanation:
Let x be the unknown positive integer.
The square roots of x are [tex]\sqrt{x}[/tex] and [tex]-\sqrt{x}[/tex], representing the positive and negative square roots respectively.
Taking the difference of those means we subtract:
[tex]\text{PositiveRoot}-\text{NegativeRoot} = \sqrt{x} - (-\sqrt{x}) = \sqrt{x}+\sqrt{x} = 2\sqrt{x}[/tex]
Set that equal to 40 and solve for x
[tex]2\sqrt{x} = 40\\\\\sqrt{x} = 40/2\\\\\sqrt{x} = 20\\\\x = 20^2\\\\x = 400[/tex]
Therefore, the integer we're after is 400.
The positive square root of such is [tex]\sqrt{x} = \sqrt{400} = \sqrt{20^2} = 20[/tex]
And the negative square root is [tex]-\sqrt{x} = -\sqrt{400} = -\sqrt{20^2} = -20[/tex]
The difference of which is:
(Positive Root) - (Negative Root) = 20-(-20) = 20+20 = 40
This helps confirm the answers.
